Problem: $h(t) = -5t^{2}+3t+1-4(g(t))$ $g(t) = t^{2}-4t$ $f(n) = -5n+4(h(n))$ $ h(g(-1)) = {?} $
Solution: First, let's solve for the value of the inner function, $g(-1)$ . Then we'll know what to plug into the outer function. $g(-1) = (-1)^{2}+(-4)(-1)$ $g(-1) = 5$ Now we know that $g(-1) = 5$ . Let's solve for $h(g(-1))$ , which is $h(5)$ $h(5) = -5(5^{2})+(3)(5)+1-4(g(5))$ To solve for the value of $h$ , we need to solve for the value of $g(5)$ $g(5) = 5^{2}+(-4)(5)$ $g(5) = 5$ That means $h(5) = -5(5^{2})+(3)(5)+1+(-4)(5)$ $h(5) = -129$